Упр.103 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 7 класс (Алгебра)

Преобразуйте в многочлен стандартного вида выражение:

1. $$(x+5)(y-7)$$
2. $$(x-1)(x+5)$$
3. $$(3x-5)(2x+7)$$
4. $$(5x^2-1)(5x+1)$$
5. $$(5m-2n)(3m+n)$$
6. $$(4x^2-x)(2x^2+3x)$$
7. $$(-2-y)(y^2+3)$$
8. $$(3a^2-b)(4a^2+3b)$$
9. $$(a-3)(a^2+4a+2)$$
10. $$(y-2z)(y^2-2yz-5z^2)$$
11. $$m(2m-1)(3m+2)$$
12. $$-6x^2(4-2x)(3x^2+11x)$$

1) $$\begin{aligned}(x+5)(y-7)&=xy-7x+5y-35.\end{aligned}$$

2) $$\begin{aligned}(x-1)(x+5)&=x^2+5x-x-5\\&=x^2+4x-5.\end{aligned}$$

3) $$\begin{aligned}(3x-5)(2x+7)&=6x^2+21x-10x-35\\&=6x^2+11x-35.\end{aligned}$$

4) $$\begin{aligned}(5x^2-1)(5x+1)&=25x^3+5x^2-5x-1.\end{aligned}$$

5) $$\begin{aligned}(5m-2n)(3m+n)&=15m^2+5mn-6mn-2n^2\\&=15m^2-mn-2n^2.\end{aligned}$$

6) $$\begin{aligned}(4x^2-x)(2x^2+3x)&=8x^4+12x^3-2x^3-3x^2\\&=8x^4+10x^3-3x^2.\end{aligned}$$

7) $$\begin{aligned}(-2-y)(y^2+3)&=-2y^2-6-y^3-3y\\&=-y^3-2y^2-3y-6.\end{aligned}$$

8) $$\begin{aligned}(3a^2-b)(4a^2+3b)&=12a^4+9a^2b-4a^2b-3b^2\\&=12a^4+5a^2b-3b^2.\end{aligned}$$

9) $$\begin{aligned}(a-3)(a^2+4a+2)&=a^3+4a^2+2a-3a^2-12a-6\\&=a^3+a^2-10a-6.\end{aligned}$$

10) $$\begin{aligned}(y-2z)(y^2-2yz-5z^2)&=y^3-2y^2z-5yz^2-2y^2z+4yz^2+10z^3\\&=y^3-4y^2z-yz^2+10z^3.\end{aligned}$$

11) $$\begin{aligned}m(2m-1)(3m+2)&=m(6m^2+4m-3m-2)\\&=m(6m^2+m-2)\\&=6m^3+m^2-2m.\end{aligned}$$

12) $$\begin{aligned}-6x^2(4-2x)(3x^2+11x)&=-6x^2(12x^2+44x-6x^3-22x^2)\\&=-6x^2(-6x^3-10x^2+44x)\\&=36x^5+60x^4-264x^3.\end{aligned}$$

Ответ

1) $$xy-7x+5y-35$$; 2) $$x^2+4x-5$$; 3) $$6x^2+11x-35$$; 4) $$25x^3+5x^2-5x-1$$; 5) $$15m^2-mn-2n^2$$; 6) $$8x^4+10x^3-3x^2$$; 7) $$-y^3-2y^2-3y-6$$; 8) $$12a^4+5a^2b-3b^2$$; 9) $$a^3+a^2-10a-6$$; 10) $$y^3-4y^2z-yz^2+10z^3$$; 11) $$6m^3+m^2-2m$$; 12) $$36x^5+60x^4-264x^3$$.